1 files changed, 323 insertions, 0 deletions
diff --git a/llvm/lib/Support/ScaledNumber.cpp b/llvm/lib/Support/ScaledNumber.cpp
new file mode 100644
index 000000000000..54d4cc33410b
--- /dev/null
+++ b/llvm/lib/Support/ScaledNumber.cpp
@@ -0,0 +1,323 @@
+//==- lib/Support/ScaledNumber.cpp - Support for scaled numbers -*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// Implementation of some scaled number algorithms.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Support/ScaledNumber.h"
+#include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/ArrayRef.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/raw_ostream.h"
+
+using namespace llvm;
+using namespace llvm::ScaledNumbers;
+
+std::pair<uint64_t, int16_t> ScaledNumbers::multiply64(uint64_t LHS,
+                                                       uint64_t RHS) {
+  // Separate into two 32-bit digits (U.L).
+  auto getU = [](uint64_t N) { return N >> 32; };
+  auto getL = [](uint64_t N) { return N & UINT32_MAX; };
+  uint64_t UL = getU(LHS), LL = getL(LHS), UR = getU(RHS), LR = getL(RHS);
+
+  // Compute cross products.
+  uint64_t P1 = UL * UR, P2 = UL * LR, P3 = LL * UR, P4 = LL * LR;
+
+  // Sum into two 64-bit digits.
+  uint64_t Upper = P1, Lower = P4;
+  auto addWithCarry = [&](uint64_t N) {
+    uint64_t NewLower = Lower + (getL(N) << 32);
+    Upper += getU(N) + (NewLower < Lower);
+    Lower = NewLower;
+  };
+  addWithCarry(P2);
+  addWithCarry(P3);
+
+  // Check whether the upper digit is empty.
+  if (!Upper)
+    return std::make_pair(Lower, 0);
+
+  // Shift as little as possible to maximize precision.
+  unsigned LeadingZeros = countLeadingZeros(Upper);
+  int Shift = 64 - LeadingZeros;
+  if (LeadingZeros)
+    Upper = Upper << LeadingZeros | Lower >> Shift;
+  return getRounded(Upper, Shift,
+                    Shift && (Lower & UINT64_C(1) << (Shift - 1)));
+}
+
+static uint64_t getHalf(uint64_t N) { return (N >> 1) + (N & 1); }
+
+std::pair<uint32_t, int16_t> ScaledNumbers::divide32(uint32_t Dividend,
+                                                     uint32_t Divisor) {
+  assert(Dividend && "expected non-zero dividend");
+  assert(Divisor && "expected non-zero divisor");
+
+  // Use 64-bit math and canonicalize the dividend to gain precision.
+  uint64_t Dividend64 = Dividend;
+  int Shift = 0;
+  if (int Zeros = countLeadingZeros(Dividend64)) {
+    Shift -= Zeros;
+    Dividend64 <<= Zeros;
+  }
+  uint64_t Quotient = Dividend64 / Divisor;
+  uint64_t Remainder = Dividend64 % Divisor;
+
+  // If Quotient needs to be shifted, leave the rounding to getAdjusted().
+  if (Quotient > UINT32_MAX)
+    return getAdjusted<uint32_t>(Quotient, Shift);
+
+  // Round based on the value of the next bit.
+  return getRounded<uint32_t>(Quotient, Shift, Remainder >= getHalf(Divisor));
+}
+
+std::pair<uint64_t, int16_t> ScaledNumbers::divide64(uint64_t Dividend,
+                                                     uint64_t Divisor) {
+  assert(Dividend && "expected non-zero dividend");
+  assert(Divisor && "expected non-zero divisor");
+
+  // Minimize size of divisor.
+  int Shift = 0;
+  if (int Zeros = countTrailingZeros(Divisor)) {
+    Shift -= Zeros;
+    Divisor >>= Zeros;
+  }
+
+  // Check for powers of two.
+  if (Divisor == 1)
+    return std::make_pair(Dividend, Shift);
+
+  // Maximize size of dividend.
+  if (int Zeros = countLeadingZeros(Dividend)) {
+    Shift -= Zeros;
+    Dividend <<= Zeros;
+  }
+
+  // Start with the result of a divide.
+  uint64_t Quotient = Dividend / Divisor;
+  Dividend %= Divisor;
+
+  // Continue building the quotient with long division.
+  while (!(Quotient >> 63) && Dividend) {
+    // Shift Dividend and check for overflow.
+    bool IsOverflow = Dividend >> 63;
+    Dividend <<= 1;
+    --Shift;
+
+    // Get the next bit of Quotient.
+    Quotient <<= 1;
+    if (IsOverflow || Divisor <= Dividend) {
+      Quotient |= 1;
+      Dividend -= Divisor;
+    }
+  }
+
+  return getRounded(Quotient, Shift, Dividend >= getHalf(Divisor));
+}
+
+int ScaledNumbers::compareImpl(uint64_t L, uint64_t R, int ScaleDiff) {
+  assert(ScaleDiff >= 0 && "wrong argument order");
+  assert(ScaleDiff < 64 && "numbers too far apart");
+
+  uint64_t L_adjusted = L >> ScaleDiff;
+  if (L_adjusted < R)
+    return -1;
+  if (L_adjusted > R)
+    return 1;
+
+  return L > L_adjusted << ScaleDiff ? 1 : 0;
+}
+
+static void appendDigit(std::string &Str, unsigned D) {
+  assert(D < 10);
+  Str += '0' + D % 10;
+}
+
+static void appendNumber(std::string &Str, uint64_t N) {
+  while (N) {
+    appendDigit(Str, N % 10);
+    N /= 10;
+  }
+}
+
+static bool doesRoundUp(char Digit) {
+  switch (Digit) {
+  case '5':
+  case '6':
+  case '7':
+  case '8':
+  case '9':
+    return true;
+  default:
+    return false;
+  }
+}
+
+static std::string toStringAPFloat(uint64_t D, int E, unsigned Precision) {
+  assert(E >= ScaledNumbers::MinScale);
+  assert(E <= ScaledNumbers::MaxScale);
+
+  // Find a new E, but don't let it increase past MaxScale.
+  int LeadingZeros = ScaledNumberBase::countLeadingZeros64(D);
+  int NewE = std::min(ScaledNumbers::MaxScale, E + 63 - LeadingZeros);
+  int Shift = 63 - (NewE - E);
+  assert(Shift <= LeadingZeros);
+  assert(Shift == LeadingZeros || NewE == ScaledNumbers::MaxScale);
+  assert(Shift >= 0 && Shift < 64 && "undefined behavior");
+  D <<= Shift;
+  E = NewE;
+
+  // Check for a denormal.
+  unsigned AdjustedE = E + 16383;
+  if (!(D >> 63)) {
+    assert(E == ScaledNumbers::MaxScale);
+    AdjustedE = 0;
+  }
+
+  // Build the float and print it.
+  uint64_t RawBits[2] = {D, AdjustedE};
+  APFloat Float(APFloat::x87DoubleExtended(), APInt(80, RawBits));
+  SmallVector<char, 24> Chars;
+  Float.toString(Chars, Precision, 0);
+  return std::string(Chars.begin(), Chars.end());
+}
+
+static std::string stripTrailingZeros(const std::string &Float) {
+  size_t NonZero = Float.find_last_not_of('0');
+  assert(NonZero != std::string::npos && "no . in floating point string");
+
+  if (Float[NonZero] == '.')
+    ++NonZero;
+
+  return Float.substr(0, NonZero + 1);
+}
+
+std::string ScaledNumberBase::toString(uint64_t D, int16_t E, int Width,
+                                       unsigned Precision) {
+  if (!D)
+    return "0.0";
+
+  // Canonicalize exponent and digits.
+  uint64_t Above0 = 0;
+  uint64_t Below0 = 0;
+  uint64_t Extra = 0;
+  int ExtraShift = 0;
+  if (E == 0) {
+    Above0 = D;
+  } else if (E > 0) {
+    if (int Shift = std::min(int16_t(countLeadingZeros64(D)), E)) {
+      D <<= Shift;
+      E -= Shift;
+
+      if (!E)
+        Above0 = D;
+    }
+  } else if (E > -64) {
+    Above0 = D >> -E;
+    Below0 = D << (64 + E);
+  } else if (E == -64) {
+    // Special case: shift by 64 bits is undefined behavior.
+    Below0 = D;
+  } else if (E > -120) {
+    Below0 = D >> (-E - 64);
+    Extra = D << (128 + E);
+    ExtraShift = -64 - E;
+  }
+
+  // Fall back on APFloat for very small and very large numbers.
+  if (!Above0 && !Below0)
+    return toStringAPFloat(D, E, Precision);
+
+  // Append the digits before the decimal.
+  std::string Str;
+  size_t DigitsOut = 0;
+  if (Above0) {
+    appendNumber(Str, Above0);
+    DigitsOut = Str.size();
+  } else
+    appendDigit(Str, 0);
+  std::reverse(Str.begin(), Str.end());
+
+  // Return early if there's nothing after the decimal.
+  if (!Below0)
+    return Str + ".0";
+
+  // Append the decimal and beyond.
+  Str += '.';
+  uint64_t Error = UINT64_C(1) << (64 - Width);
+
+  // We need to shift Below0 to the right to make space for calculating
+  // digits.  Save the precision we're losing in Extra.
+  Extra = (Below0 & 0xf) << 56 | (Extra >> 8);
+  Below0 >>= 4;
+  size_t SinceDot = 0;
+  size_t AfterDot = Str.size();
+  do {
+    if (ExtraShift) {
+      --ExtraShift;
+      Error *= 5;
+    } else
+      Error *= 10;
+
+    Below0 *= 10;
+    Extra *= 10;
+    Below0 += (Extra >> 60);
+    Extra = Extra & (UINT64_MAX >> 4);
+    appendDigit(Str, Below0 >> 60);
+    Below0 = Below0 & (UINT64_MAX >> 4);
+    if (DigitsOut || Str.back() != '0')
+      ++DigitsOut;
+    ++SinceDot;
+  } while (Error && (Below0 << 4 | Extra >> 60) >= Error / 2 &&
+           (!Precision || DigitsOut <= Precision || SinceDot < 2));
+
+  // Return early for maximum precision.
+  if (!Precision || DigitsOut <= Precision)
+    return stripTrailingZeros(Str);
+
+  // Find where to truncate.
+  size_t Truncate =
+      std::max(Str.size() - (DigitsOut - Precision), AfterDot + 1);
+
+  // Check if there's anything to truncate.
+  if (Truncate >= Str.size())
+    return stripTrailingZeros(Str);
+
+  bool Carry = doesRoundUp(Str[Truncate]);
+  if (!Carry)
+    return stripTrailingZeros(Str.substr(0, Truncate));
+
+  // Round with the first truncated digit.
+  for (std::string::reverse_iterator I(Str.begin() + Truncate), E = Str.rend();
+       I != E; ++I) {
+    if (*I == '.')
+      continue;
+    if (*I == '9') {
+      *I = '0';
+      continue;
+    }
+
+    ++*I;
+    Carry = false;
+    break;
+  }
+
+  // Add "1" in front if we still need to carry.
+  return stripTrailingZeros(std::string(Carry, '1') + Str.substr(0, Truncate));
+}
+
+raw_ostream &ScaledNumberBase::print(raw_ostream &OS, uint64_t D, int16_t E,
+                                     int Width, unsigned Precision) {
+  return OS << toString(D, E, Width, Precision);
+}
+
+void ScaledNumberBase::dump(uint64_t D, int16_t E, int Width) {
+  print(dbgs(), D, E, Width, 0) << "[" << Width << ":" << D << "*2^" << E
+                                << "]";
+}